Problem: Reduce to lowest terms: $ \dfrac{2}{3} \div - \dfrac{7}{3} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{3}$ is $- \dfrac{3}{7}$ Therefore: $ \dfrac{2}{3} \div - \dfrac{7}{3} = \dfrac{2}{3} \times - \dfrac{3}{7} $ $ \phantom{ \dfrac{2}{3} \times - \dfrac{3}{7}} = \dfrac{2 \times -3}{3 \times 7} $ $ \phantom{ \dfrac{2}{3} \times - \dfrac{3}{7}} = \dfrac{-6}{21} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-6}{21} = \dfrac{-6 \div 3}{21 \div 3} = -\dfrac{2}{7} $